Sharp Hamilton's Laplacian estimate for the heat kernel on complete manifolds

2013/05/03 by Jia-Yong Wu, Wu, Jia-Yong
Mathematics · #35K08 #58J35 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:35K08 #msc:58J35

paper · pdf · doi:10.48550/arxiv.1305.0618

9 pages, to appear in Proceedings of the AMS

arxiv created 2013/05/03 · arxiv updated 2013/05/06

Abstract

In this paper we give Hamilton's Laplacian estimates for the heat equation on complete noncompact manifolds with nonnegative Ricci curvature. As an application, combining Li-Yau's lower and upper bounds of the heat kernel, we give an estimate on Laplacian form of the heat kernel on complete manifolds with nonnegative Ricci curvature that is sharp in the order of time parameter for the heat kernel on the Euclidean space.

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